Diameter 2 properties and convexity
Trond Arnold Abrahamsen ; Petr Hájek ; Olav Nygaard ; Jarno Talponen ; Stanimir Troyanski
Studia Mathematica, Tome 233 (2016), p. 227-242 / Harvested from The Polish Digital Mathematics Library
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We present an equivalent midpoint locally uniformly rotund (MLUR) renorming of C[0,1] with the diameter 2 property (D2P), i.e. every non-empty relatively weakly open subset of the unit ball has diameter 2. An example of an MLUR space with the D2P and with convex combinations of slices of arbitrarily small diameter is also given.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:285696 
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     title = {Diameter 2 properties and convexity},
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     year = {2016},
     pages = {227-242},
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Trond Arnold Abrahamsen; Petr Hájek; Olav Nygaard; Jarno Talponen; Stanimir Troyanski. Diameter 2 properties and convexity. Studia Mathematica, Tome 233 (2016) pp. 227-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8317-4-2016/